According to the 2010 census, the city has a total area of 3.86 square miles (10.0 km2), of which 3.80 square miles (9.8 km2) (or 98.45%) is land and 0.06 square miles (0.16 km2) (or 1.55%) is water.[8]

This settlement, first platted on June 12, 1839, was originally named Newton and was established at the rapids of the Iroquois River. By 1844, it had been renamed to Rensselaer after James Van Rensselaer, a merchant from Utica, New York, who came to the area after his business failed in the Panic of 1837. He took over the land from Joseph D. Yeoman, who had established a farm some years earlier and had begun to plan the village.[9]

There were 2,336 households of which 33.4% had children under the age of 18 living with them, 44.9% were married couples living together, 14.7% had a female householder with no husband present, 5.4% had a male householder with no wife present, and 35.1% were non-families. 29.5% of all households were made up of individuals and 12.6% had someone living alone who was 65 years of age or older. The average household size was 2.42 and the average family size was 2.96.

The median age in the city was 36.6 years. 25.5% of residents were under the age of 18; 8.7% were between the ages of 18 and 24; 25.6% were from 25 to 44; 23.7% were from 45 to 64; and 16.4% were 65 years of age or older. The gender makeup of the city was 48.0% male and 52.0% female.

As of the census[4] of 2000, there were 5,294 people, 2,158 households, and 1,404 families residing in the city. The population density was 1,824.8 people per square mile (704.8/km²). There were 2,296 housing units at an average density of 791.4 per square mile (305.7/km²). The racial makeup of the city was 97.94% White, 0.32% African American, 0.21% Native American, 0.09% Asian, 0.66% from other races, and 0.77% from two or more races. Hispanic or Latino of any race were 2.53% of the population.

There were 2,158 households out of which 31.2% had children under the age of 18 living with them, 50.1% were married couples living together, 10.8% had a female householder with no husband present, and 34.9% were non-families. 31.1% of all households were made up of individuals and 15.6% had someone living alone who was 65 years of age or older. The average household size was 2.37 and the average family size was 2.98.

In the city the population was spread out with 25.3% under the age of 18, 9.4% from 18 to 24, 26.9% from 25 to 44, 20.0% from 45 to 64, and 18.5% who were 65 years of age or older. The median age was 36 years. For every 100 females there were 89.0 males. For every 100 females age 18 and over, there were 83.4 males.

The median income for a household in the city was $34,821, and the median income for a family was $43,313. Males had a median income of $33,971 versus $24,016 for females. The per capita income for the city was $20,872. About 6.6% of families and 10.0% of the population were below the poverty line, including 11.8% of those under age 18 and 8.0% of those age 65 or over.

Humid continental climate is a climatic region typified by large seasonal temperature differences, with warm to hot (and often humid) summers and cold (sometimes severely cold) winters. Precipitation is relatively well distributed year-round in many areas with this climate, while others may see a marked reduction in wintry precipitation and even a wintertime drought. The Köppen Climate Classification subtype for this climate is "Dfa". (Hot Summer Continental Climate).[10]